Optical system for multiple imaging a linear object

ABSTRACT

An optical system provides a multiple image of a linear object, the images focussed on an image array, with the images displaced both laterally and longitudinally relative to each other, a different section of each image in a contiguous, side-by-side position. The multiple imaging is obtained by a plurality of mirrors in a stacked array, the mirrors each tilted about a first axis and rotated about a second axis, the tilt and rotation increasing progressively from the front mirror. The mirrors each have a predetermined optical transmission characteristic, being a maximum for the front mirror and decreasing progressively to the rearmost mirror.

This invention relates to an optical system for multiple imaging alinear object, whereby the linear object is imaged as a number ofsections arranged side-by-side.

In imaging systems in which an image is to be scanned electronically,such as in facsimile readers for electronic transmission of printedmatter, the object, usually a line across a page of print, is imaged onto a solid state detector device, such as a charge-coupled device (CCD)array.

The difficulty and cost of making a solid state, or other type, ofimager usually increases with size. In scanning or making apparatus,imaging a thin linear section of a page, it is a practice to image on anarray having 1728 elements, for an 81/2" wide page and with 200 linesper inch resolution. The length of such an array is close to one inchthe width about one hundredth of an inch. Such dimensions result inexpensive manufactures. If the imager is of silicon, for example, thematerial uniformity, distribution of defects, processing and reliabilityin general place severe limits on the fabrication yield of imager chipswhich are long and thin. An improvement in fabrication yield would bepossible if the imager chips need not be as long as one inch, and alsoincreased in width. This would reduce cost and improve handling ability.

The present invention provides an optical system which provides for animager array which has less disparity between width and length thanwould occur if a linear object is imaged as a continuous line. Multipleimages are produced and rearranged such that the images are inside-by-side and overlapping relationship,, with different segments ofthe object in adjacent proximity. An imager can detect and reconstructan entire image of the object from the different imaged segments. Thisis obtained by a series of mirrors situated side-by-side, tilted androtated relative to each other.

The invention will be readily understood by the following description ofan embodiment, by way of example, in conjunction with the accompanyingdrawings, in which:

FIG. 1 diagrammatically illustrates the positional relationship betweenan object, a mirror, an image reflected by the mirror and the virtualimage of the object as apparently seen by an observer;

FIG. 2 illustrates diagrammatically the positioning of virtual images,with a tilted partially transmitting mirror and a non-tilted partiallytransmitting mirror;

FIG. 3 is a diagrammatic perspective view of a system embodying thepresent invention;

FIG. 4 illustrates the image as produced by the system of FIG. 3;

FIG. 5 is a diagrammatic plan view on the plane of the detectorillustrating the theoretical images as produced by the system of FIG. 3.

As illustrated in FIG. 1, if an object 10 is placed in front of a mirror11, an observer at 12 will see an image of the object 10 which isapparently behind the mirror -- at 13. The image 13 is called thevirtual image. The rays 14 and 15 from the top of the object 10, afterreflection, appear to come from the top of the virtual image 13, asindicated by the dotted lines 14a and 15a. This diagrammatic arrangementcan be used to design other imaging systems.

FIG. 2 illustrates the generation of multiple virtual images. Mirrors 20and 21 are placed in front of object 10, in a superposed relationship.The degress of optical transmission required of mirrors 20 and 21 willbe discussed later. As a particular example, mirror 20 is shown parallelto the object 10, and mirror 21 is shown pivoted about a point 22, at anangle φ23, with respect to mirror 20. The planes of mirrors 20 and 21are perpendicular to the plane of the drawing. The pivot point 22, theangle φ23, the direct distance between object 10 and the plane of themirror 20, and the orientation of mirror 21 with respect to object 10are all arbitrary. These parameters are optimized for particular imagingsystems as will be described later. By elementary principles of optics,mirror 20 produces a virtual image 24 of the object 10 at a knownlocation. Because mirror 20 is partially transmitting, rays, such asrays 26 from point 27 an object 10 can be reflected by mirror 21 andpass through mirror 20. Therefore mirror 21 can also generate a virtualimage, such as at 28, of the object 10. The virtual images 24 and 28have portions that overlap in space. For example, the segment of image28 between 29 and 30 occupies a region containing the bottom portion ofimage 24 near position 31. The overlap between images 24 and 28 can beused to reduce requirements placed on imaging systems. For example, alens needs to capture only limited portions of images 24 and 28 about aposition 32 to yield information along the whole length of object 10.Although the segment of image 28 between 29 and 30 does not coincideentirely with the bottom part of image 24, a lens with sufficient focaldepth can render good images of the overlapping segments. Quantativeestimates for particular systems will be obtained to verify the previousstatement. The principles embodied in the arrangement of FIG. 2 provideat least two advantages for imaging extended objects. First, the angularfield of view of the imaging system can be narrowed. Second, the size ofthe photosensor arrays can be reduced. Both results yield substantialcost savings for a copying or facsimile machine.

In FIG. 2, position 30 denotes the intersection of virtual image 28 witha ray 12 from the bottom of the object 10, and position 32 denotes theintersection of image 28 with image 24. If the angle φ23, is varied, thesegment of image 28 between 29 and 30 also varies in length. As aresult, different portions of image 28, examplified by that between 30and 32, can be placed near position 31. For instance, if other partiallytransmitting mirrors are placed between mirrors 20 and 21, virtualimages similar to 24 and 28 will be produced. The images will intersectimage 24 at points other than at 32. In addition, the portion of everyimage near position 31 will correspond to a different segment alongobject 10. Thus by increasing the number of such mirrors placed between20 and 21, and properly setting their positions with respect to 20 and21, virtual images of small segments all along object 10 can be locatednear 31. Any subsequent imaging system would be required to examine onlya small region about position 31 in order to yield information on thewhole of object 10.

In FIG. 2, virtual images 24 and 28 are located in the same plane thatis the plane of the Figure. To further image segments near theintersection of 24 and 28 it may be required to separate 24 and 28 in adirection perpendicular to the plane of the drawing. FIG. 3 illustratesan imaging system embodying the aforementioned principles but with anarrangement separating the images. Partially transmitting mirrors 20 and21 are set at different angles with respect to and x' axis 35, namely atangle φ₁ (23a) for mirror 20, and angle φ₂ (23b). This angulardifference causes the separate images of object 10, indicated at 36 and37, produced by mirrors 20 and 21 and lens 38, to be laterally shiftedin the manner described in conjunction with FIG. 2. The mirrors 20 and21 are also tilted with respect to the z axis 40, at angles θ₁ and θ₂respectively, and indicated at 39a and 39b. This tilting causes theimages 36 and 37 to be separated vertically in the direction of the zaxis 40. 41 represents the plane of a photosensor.

The images 36 and 37 projected on to the photosensor, appear asillustrated in FIG. 4. Because of the lateral shift between images 36and 37, it is possible to use two short imager arrays, indicated inchain dotted outline at 45a and 45b. One such array, 45a, would coverthe segment of image 36 between lines 42 and 43, the other array, 45b,for the segment of image 37 between the same lines. Signals from botharrays would provide information over an entire image. It is evidentthat the length of either photosensor array would be shorter than thatrequired to cover image 36 or 37 alone. FIG. 5 is a top view of thedetector plane, sighting nearly parallel to the z axis 40. The images 36and 37 focussed by lens 38 have a focal depth difference. Such adifference can be reduced to give sufficiently clear image details onthe plane 41, as will be shown.

The following describes the verification, and optimization, regardingthe parameters of the arrangements in FIGS. 2 and 3 for possible actualconstructions, and demonstrates that presently available imagingcomponents can produce clear images in spite of the focal depthdifference mentioned previously.

Referring to FIG. 2, let the following symbols designate thecorresponding parameters:

x_(o) = distance between object 10 and mirror 20, normal to the plane ofthe mirror;

Δx' = distance between 31 and the horizontal projection of position 29to the line 50 normal to the plane of the mirror 20;

Δx" = distance between 30 and 31;

φ = angle denoted by 23;

d = distance between 22 and the intersection of line 50 by the plane ofthe mirror 20, indicated at 51; By geometry, it can be shown that:

    Δx" = x.sub.o {2 - [1 - (d/x.sub.o) tan φ] [sec 2φ + 1] }

    Δx' = x.sub.o [(d/x.sub.o) sin 2φ - (1-cos 2φ) ]

In order to give quantative estimates, it is necessary to considerimaging systems for particular applications. For a facsimile machineusing a 22.5 mm long, 1728-element detector array, and 13 μm wideinter-element spacing, 200 lines per inch resolution requires a 9.57times reduction of a standard 215 mm wide page. To utilize thearrangements illustrated in FIGS. 2 and 3, two 864-element arraysseparated by 50 microns can be used for detection. The arrays have thesame inter-element spacing and detector cell size as those of the1728-element array. With the same 9.57 times reduction, numericalestimates can be given for the parameters used in FIG. 3. Calculationsare made for systems with different lenses, one with a 75 mm, the othera 40 mm focal length lens. These lenses are possible choices for lens 38in FIG. 3. It is assumed that the aperture of lens 38 is 10 mm, thedimensions of mirrors 20 and 21 are 25mm × 22mm, and those of thedetector plane 41, 10mm × 10mm. In Table I the following symbols areused to denote the parameters in FIG. 3:

θ₁ : angle 39a

θ₂ : angle 39b

φ₁ : angle 23a φ₂ : angle 23b

d₁ : distance between object 10 and mirror 21

d₂ : distance between mirror 21 and lens 38

Δm: maximum percent demagnification difference between portions of 36,or of 37, or between 36 and 37

Δv: maximum image depth displacement between 36 and 37 in FIG. 5

F: f-number required of the lens

                  TABLE I                                                         ______________________________________                                        LENS              75 mm       40 mm                                           ______________________________________                                        θ.sub.1                                                                        (deg.)         3.33        6.18                                        θ.sub.2                                                                        (deg.)         3.33-.067   618-0.126                                   φ.sub.1                                                                          (deg.)         0           0                                           φ.sub.2                                                                          (deg.)         4.1         7.5                                         d.sub.1                                                                              (mm)           750.0       400.0                                       d.sub.2                                                                              (mm)           42.75       22.8                                        Δm                                                                             (%)            1.2         5.0                                         Δv                                                                             (mm)           0.07        0.15                                        F-no.  8              11.5                                                    d      (mm)           107.5       107.5                                       ______________________________________                                    

The values presented in Table I are computed using the followingformulas: ##EQU1##

    Δu = 2λF.sup.2 u.sup.2 /f.sup.2

    F = f/D

where:

u: distance of an object from the principal plane of lens

v: distance of the image from the principal plane of lens

Δu: depth of field of lens

λ: wavelength of light used for illumination

f: focal length of lens

F: f-number of lens

and Δv is computed by using Δx', Δx" given previously, and the secondformula listed above.

Table I indicates it is feasible to construct an optical system,embodying the principles of this invention, to reduce the length ofphotosensor arrays needed for imaging a standard page. The principlescan be extended for example, to a system where eight mirrors similar tomirrors 20 and 21 are employed. In the latter case, eight closely spacedimager arrays each having 216 elements or 2.8 mm in length, replace thesingle 1728-element array that is commonly used for facsimile imaging.The multi-array photo-sensor, because of its reduced length, would be ofconsiderable advantage in improving device yield.

In addition to the physical arrangements proposed in the invention, thetransmission characteristics of mirrors 20 and 21, or of a combinationof any number of such mirrors, have been studied. Quantative estimatesof the transmittance and the reflectance of each mirror can becalculated with a set of formulas. It is required that the photosensorsdetect equal signal intensity reflected from each mirror through all theintervening mirrors. It is assumed that, because of the angles (Table I)between the mirrors, multiple reflection effects can be neglected in afirst approximation. When n mirrors are used, where n denotes a number,2n quantities T_(i) and R_(i) where i=1, 2....n, have to be computed.T_(i) and R_(i) denote respectively, the normalized transmittance andreflectance of the ith mirror. Referring to FIG. 3, mirror 20, the oneclosest to the object 10, would be denoted by i=1 and mirror 21, the onefarthest from 10 by i=n. Any mirrors used in between 20 and 21 would benumbered consecutively commensurate with their distance to the object.The 2n quantities T_(i) and R.sub. i are given by 2n equations. ##EQU2##where ##EQU3## denotes a product of factors such as (T_(i) ² T_(i+1) ²...T_(n-1) ²). Equations can be solved readily with the aid ofcomputers. But for a system with limited number of mirrors the solutionis easy, for example:

for n = 2

T₁ = 0.62

r₁ = 0.38

t₂ = 0

r₂ = 1.0

and

for n = 3

T₁ = 0.77

r₁ = 0.23

t₂ = 0.62

r₂ = 0.38

t₃ = 0

r₃ = 1.0

the solutions can be refined to take into account transmission loss andmultiple reflections. Such refinements are well known from establishedprinciples of optics.

What is claimed is:
 1. An optical system for multiple imaging of alinear object, comprising:-a plurality of mirrors positioned in astacked relationship facing towards an object, each mirror having apredetermined optical transmission characteristic, being a maximum atthe front mirror and a minimum at the rear mirror; each mirror tiltedabout a first axis and rotated about a second axis, said first axisparallel to the axis of the linear object and the second axis normal tothe first axis, the first and second axes in a plane normal to the axisof the light path from said object to said mirrors, said mirrors tiltedand rotated progressively from the front mirror; an image arraylaterally displaced from the axis of the light path between the objectand the mirrors; and a lens structure positioned between the mirrors andthe image array; whereby a multiplicity of images are reflected on tosaid image array, an image from each mirror, said images laterally andlongitudinally displaced, a different section of each image in acontiguous side by side position.